A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{2!}{4!} \)
\( \frac{2 \times 1}{4 \times 3 \times 2 \times 1} \)
\( \frac{1}{4 \times 3} \)
\( \frac{1}{12} \)

To subtract these radicals together their radicands must be the same:

5\( \sqrt{175} \) - 7\( \sqrt{7} \)
5\( \sqrt{25 \times 7} \) - 7\( \sqrt{7} \)
5\( \sqrt{5^2 \times 7} \) - 7\( \sqrt{7} \)
(5)(5)\( \sqrt{7} \) - 7\( \sqrt{7} \)
25\( \sqrt{7} \) - 7\( \sqrt{7} \)

Now that the radicands are identical, you can subtract them:

In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 8 workers at the company now and that's enough to staff 2 crews so there are \( \frac{8}{2} \) = 4 workers on a crew. 7 crews are needed for the busy season which, at 4 workers per crew, means that the roofing company will need 7 x 4 = 28 total workers to staff the crews during the busy season. The company already employs 8 workers so they need to add 28 - 8 = 20 new staff for the busy season.

A number in scientific notation has the format 0.000 x 10^exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:

0.0009263 in scientific notation is 9.263 x 10^-4

You have 4 out of the total of 150 raffle tickets sold so you have a (\( \frac{4}{150} \)) x 100 = \( \frac{4 \times 100}{150} \) = \( \frac{400}{150} \) = 3% chance to win the raffle.